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2 years ago

Use the drawing tool(s) to form the correct answer on the provided graph.

Mathematics

1 answer:

AlekseyPX2 years ago

5 0

The solutions to the system of equations are (-2,-6) and (4,6)

<h3>How to determine the system of equations?</h3>

We have:

-2x + y = -2

$y = -\frac12x^2 + 3x + 2$

Next, we plot the graph of both functions.

From the attached graph, the equations intersect at (-2,-6) and (4,6)

Hence, the solutions to the system of equations are (-2,-6) and (4,6)

Read more about system of equations at:

brainly.com/question/21405634

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A tank contains 1600 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the tank at the rate 2 L/min, and

goldfiish [28.3K]

Let S(t) denote the amount of sugar in the tank at time t. Sugar flows in at a rate of

(0.04 kg/L) * (2 L/min) = 0.08 kg/min = 8/100 kg/min

and flows out at a rate of

(S(t)/1600 kg/L) * (2 L/min) = S(t)/800 kg/min

Then the net flow rate is governed by the differential equation

$\dfrac{\mathrm dS(t)}{\mathrm dt}=\dfrac8{100}-\dfrac{S(t)}{800}$

Solve for S(t):

$\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{S(t)}{800}=\dfrac8{100}$

$e^{t/800}\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{e^{t/800}}{800}S(t)=\dfrac8{100}e^{t/800}$

The left side is the derivative of a product:

$\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/800}S(t)\right]=\dfrac8{100}e^{t/800}$

Integrate both sides:

$e^{t/800}S(t)=\displaystyle\frac8{100}\int e^{t/800}\,\mathrm dt$

$e^{t/800}S(t)=64e^{t/800}+C$

$S(t)=64+Ce^{-t/800}$

There's no sugar in the water at the start, so (a) S(0) = 0, which gives

$0=64+C\impleis C=-64$

and so (b) the amount of sugar in the tank at time t is

$S(t)=64\left(1-e^{-t/800}\right)$

As $t\to\infty$ , the exponential term vanishes and (c) the tank will eventually contain 64 kg of sugar.

7 0

3 years ago

Someone annnnswer pls

cupoosta [38]

Answer:

t = 16

Step-by-step explanation:

Hope this helped :]

4 0

3 years ago

Read 2 more answers

What is the system of inequalities associated with the following graph

Fynjy0 [20]

Answer:

y<3

x+y≥1

This is the system of inequalities which will give you the result shown in the graph

Answered by GAUTHMATH

6 0

3 years ago

Jon makes a map of his neighborhood for a presentation. The scale of his map is 1 inch:125 feet. How many feet do 4 inches

kap26 [50]

Answer:

Part A) $500\ ft$

Part B) $2\ in$

Step-by-step explanation:

we know that

The scale of the map is $\frac{1}{125} \frac{in}{ft}$

That means

1 in on the map represent 125 ft in the real

Part A) How many feet do 4 inches

using proportion

$\frac{1}{125} \frac{in}{ft}=\frac{4}{x} \frac{in}{ft}\\ \\x=125*4\\ \\x=500\ ft$

Part B) Jon lives 250 feet away from Max. How many inches separate Jon’s home from Max’s on the map?

using proportion

$\frac{1}{125} \frac{in}{ft}=\frac{x}{250} \frac{in}{ft}\\ \\x=250/125\\ \\x=2\ in$

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3 years ago

Last year Kristen read one fourth as many biographies as mysteries and eighteen more science fiction books than biographies. The

Minchanka [31]

Ans: She read 35 books in all.

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